The future of an iconic Giant who starred in the 2010 World Series could be decided this week, with a chance that he will be gone after 10 years in the organization.

The Giants face a Friday deadline to offer contracts to their unsigned players, and team officials have hinted they do not plan to tender a contract to closer Brian Wilson. If so, "The Beard" would become a free agent.

Sources say the Giants do not want to see Wilson go and hope a deal can be struck, though one source indicated the Giants and Wilson have not seen eye to eye on how to proceed.

Their hands are being forced by Wilson's reconstructive elbow surgery in April and a provision in the collective bargaining agreement that prevents teams from offering their players a pay cut of more than 20 percent.

Wilson, who will enter his final year of arbitration eligibility, received $8.5 million in 2012. Thus, the Giants' lowest offer could be $6.8 million.

The Giants are not inclined to offer Wilson a $6.8 million guarantee after he missed all but two games in 2012 after undergoing his second Tommy John surgery, unsure that he will be able to pitch effectively.

However, Wilson said during the postseason that he expects to be ready to pitch for the Giants on Opening Day. He continues to rehabilitate under the Giants' supervision and has not experienced any setbacks.

The Giants prefer to let Wilson become a free agent, then re-sign him with a guaranteed salary significantly less than $6.8 million, supplemented by incentives that would yield a more significant payout if he is strong enough to pitch.

Wilson reportedly is not keen on that idea and believes he deserves a higher guarantee because of all he has given the organization, including the health of his arm in pursuit of San Francisco's first World Series title two years ago.

As a free agent, Wilson could test the market. Though his chances of getting a big-league offer elsewhere seem slim, teams are flush with cash, and at least one might be willing to gamble that the 30-year-old will return to his All-Star form.

Last month, the Chicago Cubs signed former Twins starter Scott Baker to a $5.5 million contract for 2013 even though he missed all of 2012. Baker is 31 and, like Wilson, had Tommy John surgery in April, but this was Baker's first, not his second.